# Thread: Using area to evaluate the integral

1. ## Using area to evaluate the integral

Use an area to evaluate

a^2
∫ 3x dx,
a

where a > 1

Having some trouble with this, could someone explain to me how to do this?
Thanks.

2. Originally Posted by Murphie
Use an area to evaluate

a^2
∫ 3x dx,
a

where a > 1

Having some trouble with this, could someone explain to me how to do this?
Thanks.
Dear Murphie,

First draw the graph of y=3x. Since $\displaystyle \int_{a}^{a^2}3xdx$ represents the area of this graph from $\displaystyle x=a$ to$\displaystyle x=a^2$ you can get the area of the trapezium formed by the x-axis and the curve at the given region.

Hope this will give you an idea to solve the problem.

3. is the area 1/2(a)a^2 = (a^3)/2?

4. No, it is not. Go back and do what Sudharaka said!

What are the coordinates of the vertices of the trapezium (I would say "trapezoid")? What is the "height" of that trapezoid? What are the lengths of the two "bases" of the trapezoid? Do you know the formula for the area of a trapezoid?

5. Originally Posted by Murphie
is the area 1/2(a)a^2 = (a^3)/2?
Check this answer by doing the integration.

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